3 9) Use y'(3) to determine if the graph of y = 4 cos x +- is increasing or decreasing when x = 3. %3D

Q: Question 26 Find y' by implicit differentiation for 2y³+4x2 – y = x6 . - V 6x5 – 8x (A 6y2 – 1 6x+…

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Q: b) g(x) = 2sin B = A = Amplitude = T = Max = Horizontal shift = x-values of key points: A =…

A: (a) The given functions are fx=-13cos2x (b) The given function is gx=2sinx4 (c) The given function…

Q: 2) Show that: cos (0) sin (0) (6) (5) - (² Xp = Yp sin cos (0) a))) ||rp|| cos (0 - a) -||rp|| sin…

A: This answer is given below.Explanation:

Q: f(x)=(6+x^3)^cos x Explain with steps

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Q: If f(x) = 5x2 – 6e* + sin4x, then f'(0) = O a. 6 O b. -6 О с. 2 O d. -2

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Q: y" - y' - y = cos(5t) - sin(5t); y(0) = 2 and y'=5

A: Given :y''-y'-y=cos5t-sin5ty(0)=2 and y'(0)=5

Q: 10x 19) y Sin'(5x') (ans.: JI-25 x' 20) y= Cot ) (ans.: 1+ x' 6x' 21) y=tan'V4x'- 2 (ans.: (4x'-1…

A: As per guidelines we can only solve first question or first three subparts of the question, I am…

Q: | 1' cos(T +1) dr. COS

A: using the integration by parts

Q: tind the derivatiues of given functions with respect tox. 12

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Q: y^(29) for y=-cos(x)

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Q: B/ Find the value of 1. tan+e O 1 2 dx 2. tante

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Q: 5 cos? (- x), then f' ) %3D is

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Q: 5. At right is the graph of y = cos x . Using your knowledge that 3- , draw the graph of cos x sec x…

A: Given The graph of  y = cosx  We have to find the graph of  y = sec x  using  sec x = 1cos x

Q: Find f. Note that the coefficients and the constants must be exact values (no decimals).f^II (x) =…

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Q: Find f if f" (x) = 2 + cos(x), f(0) = -8, f(T/2) = 8. *(x) :

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Q: If y = cos*[sec? (30)], and (0 =) y will be equal to?

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Q: Determine the value of the serie 4∑ ((-1)^n)/(n^2) *cos(nx) at the point x=1

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Q: Find the derivative of y = x°e*. O a. y' = 3e*x2(e*+x) O b. y 3x2(e* +1) O c. y = e*x2(x+ 3) O d. y'…

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Q: y=(b+x²)* +(1+x³)*(/3x² +x – c)cos²(4x) y' =?

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Q: cos (x) J = g(x): x2

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Q: 5. (y" – y) = e-X cos(3x) %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4) If y = 2√x - 2 tan-¹ √x, then y y' = -1 1+x²

A: Given :y=2x-2tan-1x

Q: cos x )y+y'= e^(-sinx) solve the dif eq for the problem above  thanks

A: Given that  (cos x )y+y'= e^(-sinx)

Q: 3 5. y= 23x+1 %3D 2 3x+1

A: Given : y = 323x + 1

Q: Find f. f '''(x) = cos(x), f(0) = 2, f '(0) = 6, f ''(0) = 3

A: Given, f'''(x)=cos(x) Taking integration on both side f''(x)=sin(x)+A…

Q: Find f. f "(x) = 9 + cos x, f(0) = -1, f(7t/2) = 0 f(x) =

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Q: Find : y``+ 2y` + y = cos²x turn to 1-cos2x/2

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Q: 2) x² + x²³₂²2²-√²³=5πe b) xsiny-y(os₂x = xy C) (os(xy) = sin(xy) 3.2

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Q: Sin'0+ Cos 0 =-(Cos40+ 3) 4 %3D

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Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.